Functions (1.1 & 1.4)
Graphs + Factoring
Logarithms
Absolute Value
Inverses (1.7)
100
Is the following relation a function:
{(1,3), (2,4), (3,4)} ?
Explain.
Yes, each input has exactly one output and it passes the VLT.
100
Factor the following: m2+2m-24
(m+6)(m-4)
100
1.) What is the base of a common log?
2.) What is the base of a natural log?
10, e (Euler's number)
100
Solve for m: | -5 | = x
x = 5
100
Find the inverse f -1(x) of:
f(x) = -3x + 2
f-1(x) = (-x + 2) / 3
200
Does the graph below represent a one-to-one function? Explain.
No; there are more than one unique input for every output and it fails the HLT.
200
For the graph below, write the domain and range in interval notation:
Domain: x ∈ (-∞, ∞)
Range: y ∈ [-3, ∞)
200
solve for x: log2(x) +log2(4)= 3
x = 2
200
Solve for y: | 15 | = y
y = 15
200
Find the inverse f -1(x) of:
f(x) = 1/ (x - 3)
f-1(x) = (1 + 3x) / x
300
Given f(x) = 3x-2 and g(x) = -x , find f(g(-4)).
f(g(-4)) = 10
300
Given the graph below, find:
1. f(-1)
2. x when f(x) = -2
f(-1) = -2
when f(x) = -2, x = -1 and x = 2
300
Find the inverse of y = 4(x-2)
One possible answer: y = log4(x)+2
300
Solve for x: | x | > 5
(You should have two answers.)
x =5, x=-5
300
Find the inverse f -1(x) of:
f(x) = (x + 2)2 + 3 for x>2
f-1(x) = √(x - 3) - 2
400
If f(x) = -x2 + 3x and g(x) = x - 1, find f(g(x)). Simplify your answer.
f(g(x)) = -x2 + 5x - 4
400
solve for b: b2+16b +64 = 0
b = -8
400
Given the function y = aln(x), a>0,
Which axis would y = -aln(x) be reflected about?
x-axis.
400
Solve for x: | x - 3 | = 10
You should have two answers
x = -7, x= 13
400
If f(5) = 2, find f-1(2)
f-1(2) = 5
500
If f(x) = x2 - 2x , find f(f(x)). Simplify your answer.
f(f(x)) = x4 - 4x3 + 2x2 + 4x
500
Solve for a: a2+11a = -18
a = -9, a = -2
500
Sketch a graph of y = log2(x-2) including at least two points on the graph.
Easy points to calculate are: (x,y): (3, 0), (4, 1)
500
Solve for x: | x+2 | = 18
x = -20, x = 16
500
Given: f(x) = -x3 - 3 and g(x) = ∛(-x - 3).
Are f(x) and g(x) inverses of one another? Explain.
Yes, f(g(x)) = g(f(x)) = x